{"title":"Residual Life Prediction for a System Subject to Condition Monitoring and Two Failure Modes","authors":"Akram Khaleghei Ghosheh Balagh, Viliam Makis","volume":90,"journal":"International Journal of Mechanical and Mechatronics Engineering","pagesStart":955,"pagesEnd":961,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/9998559","abstract":"
In this paper, we investigate the residual life prediction
\r\nproblem for a partially observable system subject to two failure
\r\nmodes, namely a catastrophic failure and a failure due to the system
\r\ndegradation. The system is subject to condition monitoring and the
\r\ndegradation process is described by a hidden Markov model with
\r\nunknown parameters. The parameter estimation procedure based on
\r\nan EM algorithm is developed and the formulas for the conditional
\r\nreliability function and the mean residual life are derived, illustrated
\r\nby a numerical example.<\/p>\r\n","references":"[1] I. Tumer and E. Huff, \"Analysis of triaxial vibration data for health\r\nmonitoring of helicopter gearboxes,\u201d Journal of Vibration and Acoustics,\r\nvol. 125, pp. 120\u2013128, 2003.\r\n[2] V. Makis, J. Wu, and Y. Gao, \"An application of dpca to oil data for\r\ncbm modeling,\u201d European Journal of Operational Research, vol. 174,\r\nno. 1, pp. 112\u2013123, 2006.\r\n[3] X. Wang, V. Makis, and Y. M, \"A wavelet approach to fault diagnosis of\r\nagearbox under varying load conditions,\u201d Journal of Sound and Vibration,\r\nvol. 329, p. 15701585, 2010.\r\n[4] M. Kim, R. Jiang, V. Makis, and L. C., \"Optimal bayesian fault\r\nprediction scheme for a partially observable system subject to random\r\nfailure,\u201d European Journal of Operational Research, vol. 214, pp.\r\n331\u2013339, 2011.\r\n[5] R. Jiang, \"System availability maximization and residual life predictioni\r\nunder partial observations,\u201d Ph.D. thesis, University of Toroto, 2011.\r\n[6] X. Liu, J. Li, K. Al-Khalifa, A. Hamouda, andW. Coit, \"Condition-based\r\nmaintenance for continuously monitored degrading systems with\r\nmultiple failure modes,\u201d IIE Transactions, vol. 45, no. 4, pp. 422\u201335,\r\n2013.\r\n[7] V. Makis and A. Jardine, \"Optimal replacement in the proportional\r\nhazards model,\u201d INFOR, vol. 30, no. 1, pp. 172\u2013183, 1992.\r\n[8] F. Nelwamondo, T. Marwala, and U. Mahola, \"Early classifications of\r\nbearing faults using hidden markov models, gaussian mixture models,\r\nmel-frequency cepstral coefficients and fractals,\u201d International Journal\r\nof Innovative Computing Information and Control, vol. 2, no. 6, p.\r\n12811299, 2006a.\r\n[9] M. Dong and D. He, \"Hidden semi-markov model-based methodology\r\nfor multi-sensor equipment health diagnosis and prognosis,\u201d European\r\nJournal of Operational Research, vol. 178, no. 2, pp. 858\u2013878, 2007.\r\n[10] K. M. J. Jiang, R. and V. Makis, \"Maximum likelihood estimation for a\r\nhidden semi-markov model with multivariate observation,\u201d Quality and\r\nReliability Engineering International, 2012.\r\n[11] M. Kim, V. Makis, and R. Jiang, \"Parameter estimation in a\r\ncondition-based maintenance model,\u201d Statistics and Probability Letters,\r\nvol. 80, no. 21-22, pp. 1633\u20131639, 2010.\r\n[12] J. Yang and V. Makis, \"Dynamic response of residual to external\r\ndeviations in a controlled production process,\u201d Technometrics, vol. 42,\r\npp. 290\u2013299, 2000.\r\n[13] M. Kim, V. Makis, and R. Jiang, \"Parameter estimation for partially\r\nobservable systems subject to random failure,\u201d Applied Stochastic\r\nModels in Business and Industry, 2012.\r\n[14] R. Palivonaite, K. Lukoseviciute, and M. Ragulskis, \"Algebraic\r\nsegmentaion of short nonstationary time series based on evolutionary\r\nprediction algorithms,\u201d Neurocomputing, vol. 121, pp. 354\u2013364, 2013.\r\n[15] H. Aksoy, A. Gedikli, N. Unal, and A. Kehagias, \"Fast segmentation\r\nalgoirthms for long hydrometeorological time series,\u201d Hydrological\r\nProcesses, vol. 22, pp. 4600\u20134608, 2008.\r\n[16] A. Snoussi, M. Ghourabi, and M. Limam, \"On spc for short\r\nrun autocorrelated data,\u201d Communication in Statistics-Simulation and\r\nComputation, vol. 34, pp. 219\u2013234, 2005.\r\n[17] M. Ghourabi and M. Limam, \"Residual responses to change patterns of\r\nautocorrelated processes,\u201d Journal of Applied Statistics, vol. 34, no. 7,\r\npp. 785\u2013798, 2007.\r\n[18] S. Asmussen, O. Nerman, and O. M, \"Fitting phase-type distribution via\r\nthe em algorithm,\u201d Scan J Stat, vol. 23, pp. 419\u201344, 1996.\r\n[19] A. Khaleghei GB and V. Makis, \"Hsm modeling of a partially\r\nobservable system subject to deterioration and random failure using\r\nphase method,\u201d 2012. (Online). Available: http:\/\/www.mie.utoronto.ca\/\r\nresearch\/technical-reports\/reports\/report.pdf","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 90, 2014"}